Fill area behind animated line
if I got what you mean, you could toggle cyclic (ALT-C) on the 2D curve in edit mode, to get a fill. In Blender there's no concept of "object border" but you could use freestyle to obtain something usable maybe. 

Here is the overall setup from which you could start...



for the fill, you should be able to use a "Blend" texture type using also transparency, see second image example